Standard error of the mean (SE) = S/square root of n
95% confidence interval for μ = mean ± 2SE
I hope this helps. Thanks for asking.
n=100
mean=7
S=2 years
95% confidence interval for μ = mean ± 2SE
I hope this helps. Thanks for asking.
The formula for calculating the confidence interval is:
Confidence Interval = mean ± (z * (S / √n))
where 'z' is the z-score corresponding to the desired confidence level.
For a 95% confidence level, the z-score is approximately 1.96.
Plugging in the values you provided:
n = 100
mean = 7
S = 2
Confidence Interval = 7 ± (1.96 * (2 / √100))
Now, let's calculate the lower and upper bounds of the confidence interval:
Lower bound = 7 - (1.96 * (2 / √100))
Upper bound = 7 + (1.96 * (2 / √100))
Calculating these values, we get:
Lower bound ≈ 6.604
Upper bound ≈ 7.396
Therefore, the 95% confidence interval for the population mean time the postal service employees have spent with the postal service is approximately (6.604, 7.396) years.